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Properties

Label 4650.ep
Modulus 46504650
Conductor 23252325
Order 3030
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4650, base_ring=CyclotomicField(30))
 
M = H._module
 
chi = DirichletCharacter(H, M([15,27,29]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(269,4650))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 46504650
Conductor: 23252325
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 3030
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 2325.ej
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ15)\Q(\zeta_{15})
Fixed field: Number field defined by a degree 30 polynomial

Characters in Galois orbit

Character −1-1 11 77 1111 1313 1717 1919 2323 2929 3737 4141 4343
χ4650(269,⋅)\chi_{4650}(269,\cdot) 11 11 e(1730)e\left(\frac{17}{30}\right) e(215)e\left(\frac{2}{15}\right) e(1115)e\left(\frac{11}{15}\right) e(2930)e\left(\frac{29}{30}\right) e(115)e\left(\frac{1}{15}\right) −1-1 11 e(415)e\left(\frac{4}{15}\right) e(1930)e\left(\frac{19}{30}\right) e(1315)e\left(\frac{13}{15}\right)
χ4650(1469,⋅)\chi_{4650}(1469,\cdot) 11 11 e(730)e\left(\frac{7}{30}\right) e(715)e\left(\frac{7}{15}\right) e(115)e\left(\frac{1}{15}\right) e(1930)e\left(\frac{19}{30}\right) e(1115)e\left(\frac{11}{15}\right) −1-1 11 e(1415)e\left(\frac{14}{15}\right) e(2930)e\left(\frac{29}{30}\right) e(815)e\left(\frac{8}{15}\right)
χ4650(2039,⋅)\chi_{4650}(2039,\cdot) 11 11 e(1930)e\left(\frac{19}{30}\right) e(415)e\left(\frac{4}{15}\right) e(715)e\left(\frac{7}{15}\right) e(1330)e\left(\frac{13}{30}\right) e(215)e\left(\frac{2}{15}\right) −1-1 11 e(815)e\left(\frac{8}{15}\right) e(2330)e\left(\frac{23}{30}\right) e(1115)e\left(\frac{11}{15}\right)
χ4650(3959,⋅)\chi_{4650}(3959,\cdot) 11 11 e(1130)e\left(\frac{11}{30}\right) e(1115)e\left(\frac{11}{15}\right) e(815)e\left(\frac{8}{15}\right) e(1730)e\left(\frac{17}{30}\right) e(1315)e\left(\frac{13}{15}\right) −1-1 11 e(715)e\left(\frac{7}{15}\right) e(730)e\left(\frac{7}{30}\right) e(415)e\left(\frac{4}{15}\right)
χ4650(4109,⋅)\chi_{4650}(4109,\cdot) 11 11 e(130)e\left(\frac{1}{30}\right) e(115)e\left(\frac{1}{15}\right) e(1315)e\left(\frac{13}{15}\right) e(730)e\left(\frac{7}{30}\right) e(815)e\left(\frac{8}{15}\right) −1-1 11 e(215)e\left(\frac{2}{15}\right) e(1730)e\left(\frac{17}{30}\right) e(1415)e\left(\frac{14}{15}\right)
χ4650(4229,⋅)\chi_{4650}(4229,\cdot) 11 11 e(2330)e\left(\frac{23}{30}\right) e(815)e\left(\frac{8}{15}\right) e(1415)e\left(\frac{14}{15}\right) e(1130)e\left(\frac{11}{30}\right) e(415)e\left(\frac{4}{15}\right) −1-1 11 e(115)e\left(\frac{1}{15}\right) e(130)e\left(\frac{1}{30}\right) e(715)e\left(\frac{7}{15}\right)
χ4650(4289,⋅)\chi_{4650}(4289,\cdot) 11 11 e(2930)e\left(\frac{29}{30}\right) e(1415)e\left(\frac{14}{15}\right) e(215)e\left(\frac{2}{15}\right) e(2330)e\left(\frac{23}{30}\right) e(715)e\left(\frac{7}{15}\right) −1-1 11 e(1315)e\left(\frac{13}{15}\right) e(1330)e\left(\frac{13}{30}\right) e(115)e\left(\frac{1}{15}\right)
χ4650(4529,⋅)\chi_{4650}(4529,\cdot) 11 11 e(1330)e\left(\frac{13}{30}\right) e(1315)e\left(\frac{13}{15}\right) e(415)e\left(\frac{4}{15}\right) e(130)e\left(\frac{1}{30}\right) e(1415)e\left(\frac{14}{15}\right) −1-1 11 e(1115)e\left(\frac{11}{15}\right) e(1130)e\left(\frac{11}{30}\right) e(215)e\left(\frac{2}{15}\right)